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• Noetherian
  :of [[submodule]]s of <math>M</math>, there exists an integer <math>n</math> so that <math> # Every submodule <math>N</math> of <math>M</math> is [[finitely generated]] (i.e. can be wri
  3 KB (514 words) - 22:18, 10 April 2009
• Simple module
  ...mple as a [[group with operators]]&mdash;that is, it is a module with no [[submodule]]s other than itself and the zero module, and it is not itself the zero mod
  1 KB (253 words) - 11:02, 29 September 2012
• Cyclic module
  In a left <math>R</math>-module <math>M</math>, the cyclic [[submodule]] generated by an element
  695 bytes (114 words) - 16:09, 17 August 2009
• Semisimple module
  for every submodule <math>N \subset M</math>, there exists a submodule <math>N' \subset M</math> Then every [[submodule]] and [[quotient]] module of <math>M</math> is also
  6 KB (1,183 words) - 15:02, 18 August 2009
• Fractional ideal
  ...ideal''', <math>I</math>, of <math>R</math> is an <math>R</math>-[[module|submodule]] of <math>K</math> such that <math>\alpha I\subseteq R</math> for some non ...> generated by the set <math>I\cup J</math> and let <math>IJ</math> be the submodule of <math>K</math> generated by the set <math>\{xy|x\in I, y\in J\}</math>.
  2 KB (288 words) - 20:05, 23 January 2017